I did consider that, and it would make sense, though I think it would need more and heavier supports than just those small studs. Though I have used this method for other machines, I decided against it here for two reasons.
First, I was not certain I would keep the lathe in one place as I developed the workshop.
Secondly the floor below the cabinet is completely hidden by the base-plate so I could not guarantee grouting the entire cavity properly, especially since the back of the box is only a few inches from the workshop wall.
As it happens the lathe will probably stay in that location. For a start I have mounted the motor on a sub-frame fitted to a frame supporting the overhead hoist rails, so moving the machine is not just a simple matter of crow-bars and rollers. The workshop floor is reasonably smooth and level concrete but not to machine-tool accuracy, and the cabinet overlaps a rough shuttering-scar a few inches wide, along the walls.
The Harrison manual does refer to levelling screws but my lathe stand had only plain holes, so probably pre-dates that edition of the handbook.
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I have used at work an equivalent to your aircraft-engineering technique. Two specially-profiled aluminium wedge pairs had to hold a rectangular assembly to the narrow inner ends of an elliptical fibre-glass shell in such a way the wedges could be pressed in to a calculated pre-stress. The rear faces of the outer wedges were therefore machined to a close-fitting elliptical arc, but bedded into the shell itself by a similar resin compound allowed to cure under a minimal load before the full insertion. On completion the projecting wedge ends were trimmed back flush and everything stayed permanently in place – and they proved extremely difficult to dismantle safely anyway.
The biggest headache was of the wedges' bearing faces galling, so they had to be coated liberally with anti-seize grease, and usually successfully.